Natural image matting has garnered increasing attention in various computer vision applications. The matting problem aims to find the optimal foreground/background (F/B) color pair for each unknown pixel and thus obtain an alpha matte indicating the opacity of the foreground object. This problem is typically modeled as a large-scale pixel pair combinatorial optimization (PPCO) problem. Heuristic optimization is widely employed to tackle the PPCO problem owing to its gradient-free property and promising search ability. However, traditional heuristic methods often encode F/B solutions to a one-dimensional (1D) representation and then evolve the solutions in a 1D manner. This 1D representation destroys the intrinsic two-dimensional (2D) structure of images, where the significant spatial correlations among pixels are ignored. Moreover, the 1D representation also brings operation inefficiency. To address the above issues, this article develops a spatial-aware tensorial evolutionary image matting (TEIM) method. Specifically, the matting problem is modeled as a 2D Spatial-PPCO (S-PPCO) problem, and a global tensorial evolutionary optimizer is proposed to tackle the S-PPCO problem. The entire population is represented as a whole by a third-order tensor, in which individuals are classified into two types: F and B individuals for denoting the 2D F/B solutions, respectively. The evolution process, consisting of three tensorial evolutionary operators, is implemented based on pure tensor computation for efficiently seeking F/B solutions. The local spatial smoothness of images is also integrated into the evaluation process for obtaining a high-quality alpha matte. Experimental results compared with state-of-the-art methods validate the effectiveness of TEIM.